Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

A visual description of early-number counting, addition and subtraction knowledge

Early-number is a rich fabric of interconnected ideas that is often misunderstood and thus taught in ways that do not lead to rich understanding. In this presentation, a visual language is used to describe the organisation of this domain of knowledge. This visual language is based upon Piaget’s notion of reflective abstraction (Dubinsky, 1991; Piaget, 1977/2001), and thus captures the epistemological associations that link the problems, concepts and representations of the domain. The constructs of this visual language are introduced and then applied to the early-number domain. The introduction to this visual language may prompt reflection upon its suitability and significance to the description of other domains of knowledge. Through such a process of analysis and description, the visual language may serve as a scaffold for enhancing pedagogical content knowledge and thus ultimately improve learning outcomes.

Integration of CENA practice standards for postgraduate emergency nursing assessment

The use of professional competency standards to assess postgraduate nursing student’s clinical performance has been in place since 2004, at the Queensland University of Technology, School of Nursing & Midwifery (SONAM) when the Graduate Certificate in Emergency Nursing degree commenced. Emergency nursing students were assessed in their workplace, using a Clinical Performance Appraisal Tool or CPAT which was based on the Australian College of Critical Care Nurses (ACCCN) Competency Standards. With the subsequent formation of a separate Emergency Nursing Course advisory group in 2007, there was a review of clinical assessment course component. The release of the 2008 CENA revised Practice Standards for the Emergency Nursing Specialist’s, led to the emergency nursing course advisory committee supporting the integration of the CENA practice standards for assessment of emergency nurses in preference to the less relevant ACCCN competency standards. The SONAM emergency nursing study area team commenced the phasing in and progression of the CENA practice standards across the two Graduate Certificate units, and Graduate Diploma and Master of Nursing (emergency) clinical major options in 2009. As some units undertaken in the degree are available to nurses in other disciplines a separate CPAT was devised for the clinical assessments according to speciality context. The team has had to carefully consider how the professional standards are integrated into the teaching and assessment of the unit and not just applied instead of the ACCCN competency standards. Professional standards for the emergency context has also helped tailor course content and learning outcomes to be relevant across a number of emergency nursing contexts in Australia. The assessment of the CPAT is undertaken at the workplace by QUT appointed clinical lecturers. Clinical lecturers need to apply and have suitable postgraduate qualification to undertake the position. The clinical lecturer support role is well established at QUT. The integration of the new CENA practice standards has necessitated a review of the postgraduate assessment of emergency nurses. A clinical lecturer workshop has been organised to review role, scope and how to utilise the new look CENA based CPAT, clinical assessment format.

Caregiving experience and its influencing factors : rural versus urban adult-child caregivers caring for parents with dementia in China

Background: It is predicted that China will have the largest number of cases of dementia in the world by 2025 (Ferri et al., 2005). Research has demonstrated that caring for family members with dementia can be a long-term, burdensome activity resulting in physical and emotional distress and impairment (Pinquart & Sorensen, 2003b). The establishment of family caregiver supportive services in China can be considered urgent; and the knowledge of the caregiving experience and related influencing factors is necessary to inform such services. Nevertheless, in the context of rapid demographic and socioeconomic change, the impact of caregiving for rural and urban Chinese adult-child caregivers may be different, and different needs in supportive services may therefore be expected. Objectives: The aims of this research were 1) to examine the potential differences existing in the caregiving experience between rural and urban adult-child caregivers caring for parents with dementia in China; and 2) to examine the potential differences existing in the influencing factors of the caregiving experience for rural as compared with urban adult-child caregivers caring for parents with dementia in China. Based on the literature review and Kramer.s (1997) caregiver adaptation model, six concepts and their relationships of caregiving experience were studied: severity of the care receivers. dementia, caregivers. appraisal of role strain and role gain, negative and positive well-being outcomes, and health related quality of life. Furthermore, four influencing factors (i.e., filial piety, social support, resilience, and personal mastery) were studied respectively. Methods: A cross-sectional, comparative design was used to achieve the aims of the study. A questionnaire, which was designed based on the literature review and on Kramer.s (1997) caregiver adaptation model, was completed by 401 adult-child caregivers caring for their parents with dementia from the mental health outpatient departments in five hospitals in the Yunnan province, P.R. China. Structural equation modelling (SEM) was employed as the main statistical technique for data analyses. Other statistical techniques (e.g., t-tests and Chi-Square tests) were also conducted to compare the demographic characteristics and the measured variables between rural and urban groups. Results: For the first research aim, the results indicated that urban adult-child caregivers in China experienced significantly greater strain and negative well-being outcomes than their rural peers; whereas, the difference on the appraisal of role gain and positive outcomes was nonsignificant between the two groups. The results also indicated that the amounts of severity of care receivers. dementia and caregivers. health related quality of life do not have the same meanings between the two groups. Thus, the levels of these two concepts were not comparable between the rural and urban groups in this study. Moreover, the results also demonstrated that the negative direct effect of gain on negative outcomes in urban caregivers was stronger than that in rural caregivers, suggesting that the urban caregivers tended to use appraisal of role gain to protect themselves from negative well-being outcomes to a greater extent. In addition, the unexplained variance in strain in the urban group was significantly more than that in the rural group, suggesting that there were other unmeasured variables besides the severity of care receivers. dementia which would predict strain in urban caregivers compared with their rural peers. For the second research aim, the results demonstrated that rural adult-child caregivers reported a significantly higher level of filial piety and more social support than their urban counterparts, although the two groups did not significantly differ on the levels of their resilience and personal mastery. Furthermore, although the mediation effects of these four influencing factors on both positive and negative aspects remained constant across rural and urban adult-child caregivers, urban caregivers tended to be more effective in using personal mastery to protect themselves from role strain than rural caregivers, which in turn protects them more from the negative well-being outcomes than was the case with their rural peers. Conclusions: The study extends the application of Kramer.s caregiving adaptation process model (Kramer, 1997) to a sample of adult-child caregivers in China by demonstrating that both positive and negative aspects of caregiving may impact on the caregiver.s health related quality of life, suggesting that both aspects should be targeted in supportive interventions for Chinese family caregivers. Moreover, by demonstrating partial mediation effects, the study provides four influencing factors (i.e., filial piety, social support, resilience, and personal mastery) as specific targets for clinical interventions. Furthermore, the study found evidence that urban adult-child caregivers had more negative but similar positive experience compared to their rural peers, suggesting that the establishment of supportive services for urban caregivers may be more urgent at present stage in China. Additionally, since urban caregivers tended to use appraisal of role gain and personal mastery to protect themselves from negative well-being outcomes than rural caregivers to a greater extend, interventions targeting utility of gain or/and personal mastery to decrease negative outcomes might be more effective in urban caregivers than in rural caregivers. On the other hand, as cultural expectations and expression of filial piety tend to be more traditional in rural areas, interventions targeting filial piety could be more effective among rural caregivers. Last but not least, as rural adult-child caregivers have more existing natural social support than their urban counterparts, mobilising existing natural social support resources may be more beneficial for rural caregivers, whereas, formal supports (e.g., counselling services, support groups and adult day care centres) should be enhanced for urban caregivers.

An advanced meshless method for time fractional diffusion equation

Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

Natural convection flow in a porous enclosure with localized heating from below

Natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below, symmetrical cooling from the sides and the top and rest of the bottom walls are insulated, has been investigated numerically. Darcy’s law for porous media along with the energy equation based on the 1st law of thermodynamics has been considered. Implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.

Chinese driver perceptions about speeding and traffic law enforcement

The World Health Organisation has highlighted the urgent need to address the escalating global public health crisis associated with road trauma. Low-income and middle-income countries bear the brunt of this, and rapid increases in private vehicle ownership in these nations present new challenges to authorities, citizens, and researchers alike. The role of human factors in the road safety equation is high. In China, human factors have been implicated in more than 90% of road crashes, with speeding identified as the primary cause (Wang, 2003). However, research investigating the factors that influence driving speeds in China is lacking (WHO, 2004). To help address this gap, we present qualitative findings from group interviews conducted with 35 Beijing car drivers in 2008. Some themes arising from data analysis showed strong similarities with findings from highly-motorised nations (e.g., UK, USA, and Australia) and include issues such as driver definitions of ‘speeding’ that appear to be aligned with legislative enforcement tolerances, factors relating to ease/difficulty of speed limit compliance, and the modifying influence of speed cameras. However, unique differences were evident, some of which, to our knowledge, are previously unreported in research literature. Themes included issues relating to an expressed lack of understanding about why speed limits are necessary and a perceived lack of transparency in traffic law enforcement and use of associated revenue. The perception of an unfair system seemed related to issues such as differential treatment of certain drivers and the large amount of individual discretion available to traffic police when administering sanctions. Additionally, a wide range of strategies to overtly avoid detection for speeding and/or the associated sanctions were reported. These strategies included the use of in-vehicle speed camera detectors, covering or removing vehicle licence number plates, and using personal networks of influential people to reduce or cancel a sanction. These findings have implications for traffic law, law enforcement, driver training, and public education in China. While not representative of all Beijing drivers, we believe that these research findings offer unique insights into driver behaviour in China.

Idyll number eleven

This is a short horror story formulated in the research process for the novel "That Blackfella Bloodsucka Dance!"

Prandtl number scaling of natural convection of an inclined flat plate due to uniform surface heat flux

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a new Prandtl number scaling has been developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.

Creative suburbia : rethinking urban cultural policy – the Australian case

This article considers the question of whether creative workers demonstrate a preference for inner cities or suburbs, drawing upon research findings from the ‘Creative Suburbia’ project undertaken by a team of Australian researchers over 2008–2010 in selected suburban areas of Brisbane and Melbourne. Locating this question in wider debates about the relationship of the suburbs to the city, as well as the development of new suburban forms such as master-planned communities, the article finds that the number of creative industries workers located in the suburbs is significant, and those creative workforce members living and working in suburban areas are generally happy with this experience, locating in the suburbs out of personal choice rather than economic necessity. This runs counter to the received wisdom on creative cities, which emphasize cultural amenity in inner city areas as a primary driver of location decisions for the ‘creative class’. The article draws out some implications of the findings for urban cultural policy, arguing that the focus on developing inner urban cultural amenity has been overplayed, and that more attention should be given to how to better enable distributed knowledge systems through high-speed broadband infrastructure.

Symbolic number : the integration of magnitude and spatial representations in children aged 6 to 8 years

The process of learning symbolic Arabic digits in early childhood requires that magnitude and spatial information integrates with the concept of symbolic digits. Previous research has separately investigated the development of automatic access to magnitude and spatial information from symbolic digits. However, developmental trajectories of symbolic number knowledge cannot be fully understood when considering components in isolation. In view of this, we have synthesized the existing lines of research and tested the use of both magnitude and spatial information with the same sample of British children in Years 1, 2 and 3 (6-8 years of age). The physical judgment task of the numerical Stroop paradigm (NSP) demonstrated that automatic access to magnitude was present from Year 1 and the distance effect signaled that a refined processing of numerical information had developed. Additionally, a parity judgment task showed that the onset of the Spatial-Numerical Association of Response Codes (SNARC) effect occurs in Year 2. These findings uncover the developmental timeline of how magnitude and spatial representations integrate with symbolic number knowledge during early learning of Arabic digits and resolve inconsistencies between previous developmental and experimental research lines.

Representational change and strategy use in children's number line estimation during the first years of primary school

Background: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. Methods: Typically developing children (n = 67) from Years 1 – 3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. Results: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. Conclusion: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.